If [ ll x+y & 2 x+z x-y & 2 z+w ]= [ cc 4 & 7 0 & 10 ], then the … - Vidyadip

MCQ

If $\left[\begin{array}{ll}x+y & 2 x+z \\ x-y & 2 z+w\end{array}\right]=\left[\begin{array}{cc}4 & 7 \\ 0 & 10\end{array}\right]$, then the values of $x, y, z$ and $w$ respectively are

✓
2, 2, 3, 4
B
2, 3, 1, 2
C
$3,3,0,1$
D
None of these

✓

Answer

Correct option: A.

2, 2, 3, 4

(a) : Since, $\left[\begin{array}{ll}x+y & 2 x+z \\ x-y & 2 z+w\end{array}\right]=\left[\begin{array}{cc}4 & 7 \\ 0 & 10\end{array}\right]$
$\Rightarrow x+y=4$ ...(i)
$
\begin{array}{l}
x-y=0 && ...(ii) \\
2 x+z=7 && ...(iii) \\
\end{array}
$
and $2 z+w=10$ ...(iv)
On solving these equations, we get $x=2, y=2, z=3$ and $w=4$

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